I have set up my HOST->SMTP settings correctly.

However, I get the follopwing error when I click the "Test" link...

There has been an error trying to send the test email. The error is:
Mailbox name not allowed. The server response was: Sorry, relaying denied from that From address (#5.7.1)

Help Me Please.

Was I wrong in assuming that DNN could simply connect to my service provider and send the email that way?

I do not have POP or SMTP set up on my webserver, do I need to do that?

DNN piggy backs on the SMTP service setup that is either on your web server or you provide it with the server/username and password credentials for an SMTP server that allows relay. If you've not set this up, this is why you're getting the error you're seeing. It can connect to your service provider but have you setup your service provider credentials?

Sanjay